The course focuses on Statistical Signal Processing and Learning and covers the following topics:
- Review of basics: matrix and linear algebra; quadratic and constrained optimization problems.
- Introduction to the estimation problem and models: definitions, performance, sufficient statistics, linear and non-linear models.
- Estimators: best linear unbiased estimation (BLUE), maximum likelihood estimation (MLE), least squares method. Cramer Rao lower bound.
- Bayesian estimators: a-posteriori estimation (MAP, MMSE and LMMSE); Wiener filter; linear prediction and Yule-Walker equations.
- Adaptive filters: LMS, RLS methods, convergence analysis and step-size selection.
- Bayesian tracking: dynamic model and Kalman filter; examples of positioning.
- 2D signals properties and physical filters
- Array processing: and direction of arrivals (DOA), beamforming methods.
- Pattern and sequence recognition: Bayesian classification of signals in noise, linear discriminant, PCA and clustering methods, supervised classification, deep learning methods and updates.
- Montecarlo simulation: and numerical analysis on some use cases.
Google is involved in the laboratory activity.